Workpiece manipulating apparatus and turning spool therefor

ABSTRACT

In an apparatus for manipulating an elongated workpiece, a plurality of spools are transversely mounted along the length of a fixture for rotation about spaced axes. Each spool includes a peripheral work-engaging surface which is contoured so as to cause the workpiece to turn about an axis in a plane substantially normal to the axis of rotation of the spool as the spool is rotated.

United States Patent [191 Parris May 22,1973

[54] WORKPIECE MANIPULATING APPARATUS AND TURNING SPOOL THEREFOR [75] Inventor: John L. Parris, Knoxville, Tenn.

[73] Assignee: The Carborundum Company, Niagara Falls, NY.

[22] Filed: Feb. 12, 1971 21 Appl. No.: 114,932

[52] US. Cl. ..214/1 QG, 51/236 [51] Int. Cl ..B65g 7/00 [58] Field of Search ..214/1 QG, 340; 51/236, 216

[56] References Cited UNITED STATES PATENTS 3,472,397 10/1969 Rhoads ..2l4/1QG FOREIGN PATENTS OR APPLICATIONS 881,136 11/1961 GreatBritain ..2l4/lQG 136,696 5/1960 U.S.S.R. ..214/1QG Primary Examiner-Harold D. Whitehead Attorney-David E. Dougherty and Robert E. Walter [57] ABSTRACT In an apparatus for manipulating an elongated workpiece, a plurality f spools are transversely mounted along the length of a fixture for rotation about spaced axes. Each spool iiicludes a peripheral work-engaging surface which is ontoured so as to cause the workpiece to turn about an axis in a plane substantially normal to the axis of rotation of the spool as the spool is rotated.

23 Claims, 11 Drawing Figures Patented May 22, 1973 4 Sheets-Sheet 1 IN'VENTOR,

JOHN L. PARRIS BY fi odaf Ma Patented May 22, 1973 4 Sheets-Sheet 2 W. L W

.. M 6 1 J W fin 3 ill Patented May 22, 1973 3,734,305

4 Sheets-Sheet P;

FIG. 7 FIG. IO \VENTOR.

JOHN L. PARRIS BY comra wwa Patented May 22, 1973 3,734,305

4 Sheets-Sheet 4 INVENTOR.

JOHN L. PARRIS WORKPIECE MANIPULATING APPARATUS AND TURNING SPOOL THEREFOR BACKGROUND OF THE INVENTION In manufacturing, it is often necessary to manipulate a workpiece to perform processes thereon or for inspection. This problem is particularly acute in the manufacture of metals where heavy billets are manipulated during grinding operations for the removal of scale or surface imperfections, such as cracks and seams which adversely affect the finished product.

In the past various devices employing many moving parts have been devised to position and turn billets. In one assembly of the prior art, the billet is turned by a plurality of fingers pushing upwardly against the inside of the billet resting on a table. The fingers are positioned forward the center of gravity of the billet so that the billet falls on another side as the fingers are projected to produce a 90 rotation. In this type of device, the billet is securely supported only when lying with a side flat against the table. During rotation, the billet is either leaning against the ends of the fingers or falling onto another side. Therefore, the workpiece cannot be effectively processed in these intermediate positions.

In another type of complicated turning device of the prior art, a plurality of clamps and supporting arms are employed at each supporting position along the length of the billet. Each clamp or arm moves in a manner that must be coordinated with the movements of the other arms or clamps during the tilting and turning of the workpiece. Due to the size and weight of billets, each of the moving parts are subjected to large stresses and strains.The many moving parts under high stresses greatly increase the risk of machine breakdown. The malfunction or breakage of a single part can result in long delays in production while that part is being located and repaired or replaced.

Heretofore, billet turning devices have been ineffective in utilizing a simple movement of a work-engaging means which firmly supports a billet during the entire turn.

SUMMARY OF THE PRESENT INVENTION Apparatus for turning a workpiece according to the present invention, includes a plurality of spools for supporting and turning a workpiece. Means support the spools for rotation about spaced axes. Each spool has a peripheral surface for engaging a workpiece. The peripheral surface is contoured so as to turn a workpiece in engagement therewith about an axis in a plane substantially normal to the axis of rotation of the spool.

The present invention, also contemplates a turning spool for the aforementioned device.

The preferred embodiment comprises an improved apparatus for manipulating a workpiece by a simple movement of a work-engaging means which supports the workpiece during the turning thereof. The apparatus is strong, durable, and simple in construction and operation.

BRIEF DESCRIPTION OF THE DRAWINGS The drawings which illustrate a preferred embodiment of the present invention are as follows:

FIG. 1 is a top elevational view of the billet manipulating apparatus;

FIG. 2 is a side elevational view of the billet manipulating apparatus;

FIG. 3 is a perspective view of a spool;

FIG. 4 is a top elevational view of a portion of the billet manipulating apparatus and a billet;

FIGS. 5-10 are front elevational views of a spool and billet at various positions during rotation of the spool; and

FIG. 11 is a perspective view of a device used for making a spool.

DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT As illustrated in FIG. 1, a billet manipulator, generally indicated at 11 is supported for movement by wheels 13. This feature permits positioning the billet or workpiece 12 in different locations for various operations such as loading, grinding, inspecting, and unloading. A conventional loading apparatus can be used so that a billet falls lengthwise onto the billet manipulator 11. Many arrangements of grinding machines with billet manipulators are known in the prior art so that no further explanation of a grinding operation is necessary. A conveyor or platform adjacent the billet manipulator 11 can be used to receive a discharged billet 12.

Although the billet manipulator 11 as illustrated in the drawings includes a plurality of wheels 13 mounted on the lower portion of a fixture or frame 15, it should be understood that the frame 15 can be any suitable supporting means which can rest directly on the floor or ground.

A plurality of spools 17-20 are spaced longitudinally along and positioned above the frame 15 for rotation about substantially parallel axes which are transverse to the frame 15. Each spool 17-20 includes radial end surfaces 23 and 24 with axles 25 and 27 firmly engaging each end 23, 24 thereof and projecting outwardly along the axis of rotation.

A plurality of support members 29 are arranged in pairs each of which is spaced longitudinally along the frame 15. Each pair of members 29 includes opposing members 29 which are rigidly mounted on either side of the frame 15. The upper portion of each of the members 29 includes an opening 31 therein housing heavy duty bearings (not shown) which journal the axles 25 and 27 for rotation of the spools 17-20. The members 29 extend above the frame so that the spools l7-20 are free to rotate about spaced axes which lie in substantially a common horizontal plane.

The billet manipulator 11 is provided with a means for rotating the spools 17-20 together so that they effectively coact to turn a workpiece or billet 12. Each of the spools 1720 is provided with one axle 25 which includes a portion extending through openings 31 on one side of the frame 15. Exterior to the support members 29 a plurality of wheels 33 are mounted on the axle 25.

Each of the wheels 33 which includes a plurality of sprockets is connected to one of a plurality of endless linked chains 35. One of the chains 39 connects one of the wheels 33 associated with spool 17 to one of the wheels 33 associated with spool 18. Another of the wheels 33 associated with spool 18 is similarly connected to one of the wheels 33 associated with spool 19. The chains 39 are trained over the plurality of spaced sprockets of the wheels 33 and connect one of the spools 17-20 to another thereby rotating the spools 17-20 together and simultaneously.

A suitable drive means 21, such as an electric motor,

' drives a drive wheel 39. Preferably a speed reducer or gear box 41 is connected between the drive means 37 and drive wheel 39. The drive wheel 39 is connected to one of the wheels 33 of spool 17 by a chain 43. Preferably the power from a single drive means 41 is transmitted to each of the spools 17-20.

Since each of the turning spools 17-20 of the billet manipulator 11 is similar in shape and construction, it is believed that the following description of only one spool 18 such as illustrated in FIGS. 3-10 will suffice.

According to the principles of the present invention, the spool 18 includes a peripheral surface 45 which is contoured so as to cause a workpiece 12 in contact therewith to turn about an axis 47 in a plane substantially normal to the axis 49 of rotation of the spool 18 as the spool 18 is rotated.

As the spool 18 is turned a contacting portion 51 of the peripheral surface 45 is presented for engaging the workpiece 19 at each increment of rotation of the spool 18. The contacting portion 51 is preferably substantially a line support, as illustrated in FIG. 3 by a broken line. Due to irregularities in shape of the peripheral surface 45 and depending on the shape of the workpiece 12, the portion of the contacting portion 51 actually engaging the workpiece can vary.

FIGS. 5-10 illustrate the billet or workpiece 12 in different positions during the turning thereof which correspond to the rotation of the spool 18. The contacting portion 51 is formed within one or both of a pair of intersecting planes which form an angle beta (B) with an apex 53. The line formed by the intersection of the planes lies in a plane which is substantially normal to the axis 49 of rotation of the spool 18. One plane forms an angle theta (6) with respect to the axis 49 of rotation of the spool 18. The angle theta changes as the spool 18 is rotated thereby resulting in a turning of the workpiece 12 through an angle theta.

As the angle theta increases the apex 53 of the angle beta which substantially corresponds to the point of shortest radial dimension of concavity moves from one side of the spool 18 to the other side so as to cradle a corner of the workpiece 12. The point of shortest radial dimension of concavity and the apex 53 progress continuously from one end of the spool 18 to the other end as the spool 18 is rotated, so as to describe an arc 55 which is preferably substantially an arc 55 of a circle. As the apex 53 moves from one side of the are 55 to the other side, the dimensions of the contacting portion 51 formed within the intersecting planes changes. The length of the contacting portion 51 in one increases and the length thereof in the other plane decreases so that the workpiece 12 is supported by the contacting portion 51 during rotation of the spool 18.

In the position shown in FIG. 6, the angle theta is increasing and the apex 53 is moving to the respective position shown in FIG. 7 wherein the workpiece 12 has completed a turning through the angle theta. In FIGS. 8-10 the workpiece 12 is turning from a position in FIG. 8 where a corner of the billet 12 is exposed to a position in FIG. where another side 57 is exposed for processing. The position of the spool 18 in FlG. 10 represents a 360 rotation thereof so as to return the spool 18 to the position illustrated in FIG. 5. Further rotation of the spool 18 from the position shown in FIG. 10 results in a further turning of the billet 12 thereby exposing new corners and sides for processing.

The peripheral or camming surface 49 is characterized by being free from planes and is generally a concave surface resulting from the intersection of a solid body of revolution revolving about a longitudinal axis with a pair of intersecting planes. The intersection of the planes forms a line in a plane substantially normal to the axis of rotation of the spool 18 and the angle beta formed thereby is inscribed within an arc 55 within a plane passing through the axis of rotation or parallel thereto. The arc 55 extends from one end of the spool to the other so that each end thereof is a substantially equal radial distance from the axis of rotation 49. The apex 53 of the angle beta moves from one end of the arc 55 to the other end thereof along the are 55 relative to the rotation of the solid body to carve out a contoured surface 45. a

The portion of spool 18 between ends 23,24 on the member integral with ends 23,24 comprises a pair of intersecting frustums having the small ends thereof joined and the cones thereof skewed. The skewing or twisting of the frustums is such that camming surface 9 turns workpiece 12. The pair of frustums are arranged in a reverse mirror image relation so that lines of projection pass perpendicular to an axis of symmetry. The axis of symmetry which is perpendicular to axis 49 substantially passes through apex 53 when apex 53 is positioned at the bottom of are 55. The reverse mirror image results from oblique lines of projection passing through the axis of symmetry.

As illustrated in the drawings, the spool 18 is preferably shaped for accommodating billets 12 of a rectangular shape although billets 12 of varying shapes may be turned thereby. For turning rectangular or square billets 12 the angle beta is preferably about so that the contacting portion 51 fully supports the workpiece 12 across its entire bottom surface during rotation thereof. This angle beta is preferably inscribed within a semicircle which lies within a plane passing through the axis 49 or a plane parallel thereto and within a cylindrical body of revolution. The apex 53 preferably moves along the semicircle from one side thereof to the other at the rate of 1 for every 2 of rotation of the spool. Thus, for a 360 turn of the spool 18 the apex 53 has moved 180 along the arc 55 of the semicircle and the workpiece 12 has turned 90.

The spool 18 includes radial end portions 23,24 which are substantially flat and circular. As illustrated in FIG. 5, the axis 49 of rotation is preferably parallel to or on a line joining the centers of the end portions 23,24. With the axis 49 spaced from a line joining the two centers, the contoured surface 45 is deeper thereby the contacting portion 51 is greater in length. The depth of the contoured surface is limited since the structural strength of the spool 18 is weakened as more material is removed by making a deeper contour.

Although a spool having an angle beta of about 90 is preferred, the angle beta may be an angle other than 90. For example, if it is desired to rotate one side of a hexagon workpiece through an angle of 60, while providing maximum support of a contacting portion 51, the angle beta can be In this latter case, the arc 55 which is inscribed in a plane would be 120. It is contemplated that this latter variation of the contoured work-engaging surface 49 and other variations thereof are within the scope of the present invention.

The spool 18 of the present invention may be manufactured by one of several methods. In one method, a

pointed cutting tool may be utilized in conjunction with an automatic cutting machine. The mathematical equations which represent the contoured surface 45 may be programmed into the cutting machine. As the cylindrical body is rotated the cutting tool will vary its distance from the axis 49 of rotation according to the program and cut the spool 18 into the desired shape.

In another method, the spool 18 is cut from a solid cylinder 59. An apparatus used for this purpose is illustrated in FIG. 11. A frame 67 has vertically extending walls 69 which each have an opening 71 for receiving axles 25 and 27. The tops 73 of the walls 69 lie in a plane parallel to the axis 47. A pair of pins 75 each are in a plane normal to the plane containing tops 73 and spaced radially from the axis 47. One of the pins 75 is attached to each of the flat tops 73 so as to extend upwardly. A template 77 having a concave curvature in the shape of a semicircle is placed between the tops 73 so that the curve extends between the pins 75. An angle 79 is positioned over the curved template 77 so that the apex of the angle 79 is free to move along the semicircle.

To form the contoured surface 45 the angle 79 is moved from a first position where the apex is at a pin 75 and a straight line is formed between the pins to a second position where the apex of the angle 79 is moved 2 along the semicircle and the spool is rotated four degrees. A saw 81 cutting in a plane normal to the surface formed by the tops 73 cuts that portion of the spool lying outside the angle 79. The spool is then rotated another increment and the angle 79 moved along the arc and another cut is made. By this method the contoured surface is formed by a plurality of straight cuts into the surface of the spool.

Adjacent the ends of the surface 45 the spool 18 is provided with a flanged portion 83 at one end thereof. Spool 18 is provided with a plurality of flanges 83 which project outwardly from the end at those positions in which it is desired to clamp the workpiece 12. As illustrated in FIG. 5, one flange 83 projects upwardly adjacent a horizontal contacting portion and in FIG. 8 another flange 83 projects upwardly adjacent a contacting portion 51 wherein the angle theta is 45. In one position, rectangular billets 12 can be clamped against a flange with a flat side resting on the spool 18 and a flat upper surface exposed for grinding. In the other position shown in FIG. 8, the billet 12 can be clamped so as to grind a corner.

The billet manipulator 11 is also provided with a clamping and discharging mechanism 87. The clamping and discharging mechanism 87 includes a member 89 having an inclined surface 91 which engages a workpiece transverse thereto and pushes the workpiece upwardly and outwardly. The member 89 is pivotally mounted to the frame for rotation about a fixed axis. A crank arm 91 is attached to an axial portion of the clamping member below the frame 23. The crank arm 91 is connected to a fluid cylinder 93 which actuates member 87 for turning. The member 87 is provided with an abutment 95 on the top portion thereof which engages the billet 19 to either clamp or push the billet 12 off the frame 15. When the spool 18 is in clamping position with a flange 83 projecting upwardly, actuation of the clamping and discharging mechanism 87 acts to clamp the billet in between abutment 95 and the flange 87, as illustrated in FIG. 4. When the flange 87 is a nonexposed position or a smooth surface is presented to the workpiece 12, the workpiece 12 is pushed off the frame by actuation of the clamping and discharging mechanism 87.

The clamping and discharging mechanism is further described in copending application Ser. No. 114,913 entitled Apparatus for Clamping and Discharging a Workpiece, By John L. Parris and Herman J. Oldham filed on the same date as the present application.

In a grinding operation, the billet 12 is loaded onto the billet manipulator 11. The manipulator 11 is moved along a track to position it for a grinding operation. With a flat contacting surface exposed, the billet 12 is clamped by actuation of the clamping mechanism. The grinding mechanism grinds the top flat surface of the billet 12. Then the drive means 37 is actuated to rotate the spools 17-20 thereby turning the billet 12 until a corner is exposed. The billet 12 is clamped and the corner ground. Then the billet 12 is turned, clamped and ground until all the sides and corners have been processed. When the billet has been completely processed the spools 17-20 are turned to an intermedial position and the discharging mechanism 87 pushes the billet 12 onto an unloading platform.

While the preferred embodiment of the invention has been illustrated and described, it will be apparent to those skilled in the art that changes may be made in the disclosed apparatus without deviating from the invention as set forth in the following claims.

What is claimed is:

1. An apparatus for manipulating an elongated workpiece comprising a plurality of spools for supporting and turning the workpiece along the length thereof, means supporting said spools for rotation about spaced axes, each spool having a camming surface for engaging a workpiece, said camming surface contoured to turn the workpiece in engagement therewith about an axis in a plane substantially normal to the axis of rotation of said spool, said camming surface having substantially the shape resulting from the intersection of a solid body rotating about an axis of rotation and a pair of intersecting planes, said planes being oblique to the axis of rotation and forming an angle, the apex of said angle moving across the body in an arcuate path as the body is rotated.

2. An apparatus according to claim 1 wherein said axes are substantially parallel.

3. An apparatus according to claim 1 comprising means for turning said spools together. 4. An apparatus according to claim 2 wherein said supporting means includes an elongated frame, a plurality of members positioned on opposite sides of said frame along the length thereof, and said spools having axles journaled for rotation in said members.

5. An apparatus according to claim 4 including a wall at one end of said frame for blocking lengthwise movement of the workpiece as said spools are turned.

6. An apparatus according to claim 4 wherein said axles on one side of said frame have a portion extending exterior to said members and a driven wheel mounted on the extended portion of each axle.

7. An apparatus according to claim 6 wherein said turning means includes a drive wheel, means for driving said drive wheel, and means operatively connecting said drive wheel and said driven wheels for turning said spools simultaneously.

8. An apparatus according to claim 1 wherein each spool includes a flane portion at one end thereof, said flange portions being adjacent respective members on one side of said frame.

9. An apparatus according to claim 8 including means for clamping the workpiece against said flange portions.

10. A spoolfor turning a workpiece comprising end portions and a concave camming surface between said end portions, said surface contoured to turn a workpiece in engagement therewith about an axis in a plane substantially normal to the axis of rotation of said spool, said camming surface having substantially the shape resulting from the intersection ofa solid body rotating about an axis of rotation and a pair of intersecting planes, said planes being oblique to the axis of rotation of said body and forming an angle, the apex of said angle moving across the body in an arcuate path as the body is rotated.

11. A spool according to claim 10 wherein the point of shortest radial dimension of concavity moves substantially along an arc from one end of the spool to the other end, as the 'spool is rotated.

12. A spool according to claim 10 wherein said peripheral surface engages the workpiece along a contacting portion, said contacting portion varies as the spool is rotated.

13. A spool according to claim 12 wherein said contacting portion is substantially within a pair of intersecting planes.

14. A spool according to claim 12 wherein said contacting portion varies as the spool is rotated from engaging the workpiece in a plane substantially parallel to the axis of rotation of said spool at a first position to engaging the workpiece within a plane oblique to axis of rotation in a second position.

15. A spool according to claim l3wherein said contacting portion varies as the spool is rotated from engaging the workpiece within a plane substantially parallel to the axis of rotation of said spool at a first position to engaging the workpiece within a pair of intersecting oblique planes.

16. A spool according to claim 15 wherein the intersecting oblique planes form an angle, the apex of said angle moving across the spool to vary the contacting portion as the spool is rotated.

17. A spool according to claim 16 wherein the angle is inscribed within an arc and the apex of the angle moves across the spool, said arc extends from one end of said spool to the other.

18. An apparatus according to claim 17 wherein said arc comprises substantially a semicircle.

19. An apparatus according to claim 18 wherein said angle comprises substantially a right angle.

20. A spool comprising end portions, a member integral with said end portions having a camming surface, the camming surface being shaped like a pair of intersecting skewed frustrums, said camming surface having substantially the shape resulting from the intersection of a solid body rotating about an axis of rotation and a pair of intersecting planes, said planes being oblique to the axis of rotation of said body and forming an angle,

the apex of said angle moving across the body in an arcuate path as the body is rotated.

21. A spool according to claim 20 wherein the frustums have the small ends thereof joined and the cones thereof skewed.

22. A spool according to claim 21 wherein the frustums are skewed so as to turn a workpiece in engagement therewith about an axis in a plane substantially normal to the axis of rotation of said spool.

23. A spool according to claim 10 wherein the apex of said angle forms a point of shortest radial dimension of concavity, said point of shortest radial dimension of concavity progressing from one end of the spool to the other asthe spool is rotated. 

1. An apparatus for manipulating an elongated workpiece comprising a plurality of spools for supporting and turning the workpiece along the length thereof, means supporting said spools for rotation about spaced axes, each spool having a camming surface for engaging a workpiece, said camming surface contoured to turn the workpiece in engagement therewith about an axis in a plane substantIally normal to the axis of rotation of said spool, said camming surface having substantially the shape resulting from the intersection of a solid body rotating about an axis of rotation and a pair of intersecting planes, said planes being oblique to the axis of rotation and forming an angle, the apex of said angle moving across the body in an arcuate path as the body is rotated.
 2. An apparatus according to claim 1 wherein said axes are substantially parallel.
 3. An apparatus according to claim 1 comprising means for turning said spools together.
 4. An apparatus according to claim 2 wherein said supporting means includes an elongated frame, a plurality of members positioned on opposite sides of said frame along the length thereof, and said spools having axles journaled for rotation in said members.
 5. An apparatus according to claim 4 including a wall at one end of said frame for blocking lengthwise movement of the workpiece as said spools are turned.
 6. An apparatus according to claim 4 wherein said axles on one side of said frame have a portion extending exterior to said members and a driven wheel mounted on the extended portion of each axle.
 7. An apparatus according to claim 6 wherein said turning means includes a drive wheel, means for driving said drive wheel, and means operatively connecting said drive wheel and said driven wheels for turning said spools simultaneously.
 8. An apparatus according to claim 1 wherein each spool includes a flane portion at one end thereof, said flange portions being adjacent respective members on one side of said frame.
 9. An apparatus according to claim 8 including means for clamping the workpiece against said flange portions.
 10. A spool for turning a workpiece comprising end portions and a concave camming surface between said end portions, said surface contoured to turn a workpiece in engagement therewith about an axis in a plane substantially normal to the axis of rotation of said spool, said camming surface having substantially the shape resulting from the intersection of a solid body rotating about an axis of rotation and a pair of intersecting planes, said planes being oblique to the axis of rotation of said body and forming an angle, the apex of said angle moving across the body in an arcuate path as the body is rotated.
 11. A spool according to claim 10 wherein the point of shortest radial dimension of concavity moves substantially along an arc from one end of the spool to the other end, as the spool is rotated.
 12. A spool according to claim 10 wherein said peripheral surface engages the workpiece along a contacting portion, said contacting portion varies as the spool is rotated.
 13. A spool according to claim 12 wherein said contacting portion is substantially within a pair of intersecting planes.
 14. A spool according to claim 12 wherein said contacting portion varies as the spool is rotated from engaging the workpiece in a plane substantially parallel to the axis of rotation of said spool at a first position to engaging the workpiece within a plane oblique to axis of rotation in a second position.
 15. A spool according to claim 13 wherein said contacting portion varies as the spool is rotated from engaging the workpiece within a plane substantially parallel to the axis of rotation of said spool at a first position to engaging the workpiece within a pair of intersecting oblique planes.
 16. A spool according to claim 15 wherein the intersecting oblique planes form an angle, the apex of said angle moving across the spool to vary the contacting portion as the spool is rotated.
 17. A spool according to claim 16 wherein the angle is inscribed within an arc and the apex of the angle moves across the spool, said arc extends from one end of said spool to the other.
 18. An apparatus according to claim 17 wherein said arc comprises substantially a semicircle.
 19. An apparatus according to claim 18 wherein said angle comprises substantially a right angle.
 20. A spool comprising end portiOns, a member integral with said end portions having a camming surface, the camming surface being shaped like a pair of intersecting skewed frustrums, said camming surface having substantially the shape resulting from the intersection of a solid body rotating about an axis of rotation and a pair of intersecting planes, said planes being oblique to the axis of rotation of said body and forming an angle, the apex of said angle moving across the body in an arcuate path as the body is rotated.
 21. A spool according to claim 20 wherein the frustums have the small ends thereof joined and the cones thereof skewed.
 22. A spool according to claim 21 wherein the frustums are skewed so as to turn a workpiece in engagement therewith about an axis in a plane substantially normal to the axis of rotation of said spool.
 23. A spool according to claim 10 wherein the apex of said angle forms a point of shortest radial dimension of concavity, said point of shortest radial dimension of concavity progressing from one end of the spool to the other as the spool is rotated. 